The locus of the foot of perpendicular drawn from the centre of the ellipse ${x^2} + 3{y^2} = 6$ on any tangent to it is :
$\left( {{x^2} + {y^2}} \right) ^2 = 6{x^2} + 2{y^2}$
$\left( {{x^2} + {y^2}} \right) ^2 = 6{x^2} - 2{y^2}$
$\left( {{x^2} - {y^2}} \right) ^2 = 6{x^2} + 2{y^2}$
$\left( {{x^2} - {y^2}} \right) ^2 = 6{x^2} - 2{y^2}$
